BGE: Getting rigged door mesh to update for collisions
After some consideration, I've decided that my original approach is not a good way to make door rigs, even if reinstancePhysicsMesh() can be made to work for this use.

I am posting a partial answer, with what I believe to be a better way to make rigged doors. This solution assumes that armature deform is not a requirement for the doors.

The answer is partial because it does not address how to use reinstancePhysicsMesh(), but maybe someone else can post an answer addressing that aspect, or maybe it should be a separate question.

Essentially, all I did is separate the mesh into 2 objects, remove the vertex groups, and parent the entire door objects again from Pose Mode. No armature deformation, since the door panels are completely rigid. 





I realize this contradicts my original statement about wanting a single mesh, but I've realized 2 things that make managing doors with multiple parts easier:


If the parent armature of the door and the door mesh objects each have their origins at the same location it's easier to keep track of them. Grouping them together would also be a good idea, of course.
Writing the game logic on a single mesh object and then separating its parts can save you from having to write duplicate logic.


These things become obvious once thought through and tried. Together they eliminate any reason for an aversion to multi-mesh door rigs. Managing large numbers of doors each with multiple mesh objects is actually not so difficult to organize. This brings me to a third point:


Texturing as a single mesh and then separating into multiple mesh objects can simplify production too.


tl;dr I believe this approach is totally sufficient unless you have a door made of meat or something, in which case we're back to needing reinstancePhysicsMesh(). For rigid doors, this covers it.